Eur. Phys. J. Special Topics 228, 1793-1808 (2019)
https://doi.org/10.1140/epjst/e2019-800224-7

Regular Article

Periodic motions and chaos in power system including power disturbance

School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, P.R. China

^a e-mail: huangdeng9@sjtu.edu.cn

Received: 11 December 2018
Received in final form: 22 January 2019
Published online: 25 September 2019

Abstract

Single-machine infinite-bus power system is a nonlinear dynamic system with state variable in the sinusoidal function. With traditional analytical approaches, it is difficult to analyze such a nonlinear system since the rotor angle difference cannot always stay in an infinitesimal small value. In this paper, a single-machine infinite-bus power system with power disturbance will be discussed. The implicit discrete maps approach will be applied to solve the periodic motions for such a power system, and the stability condition will be discussed. The analytical expressions for periodic motions for such a single-machine infinite-bus power system can be recovered with a series of Fourier functions. The bifurcation diagram for such a system will be given to show the complexity of the motions when the frequency of the disturbance varies, and 2-D parameter map for chaotic motion will be obtained by calculating the Kolmogorov-Sinai entropy density. From analytical bifurcation for period-1 and period-2 motions, the evolution process of the periodic motion to chaos can be analytically explained.